Zobrazeno 1 - 10
of 172
pro vyhledávání: '"Sabbah, Claude"'
Autor:
Lopez, Ricardo Garcia, Sabbah, Claude
We define a Hodge-theoretical refinement of the Lyubeznik numbers for local rings of complex algebraic varieties. We prove that these numbers are independent of the choices made in their definition and that, for the local ring of an isolated singular
Externí odkaz:
http://arxiv.org/abs/2407.10010
Autor:
Sabbah, Claude
After making correct, and then improving, our definition of the category of irregular mixed Hodge modules thanks to Mochizuki's recent results arXiv:2108.03843, we show how these results allow us to obtain Kodaira-Saito-type vanishing theorems for th
Externí odkaz:
http://arxiv.org/abs/2401.00968
Autor:
Sabbah, Claude
This text surveys cohomological properties of pairs $(U,f)$ consisting of a smooth complex quasi-projective variety $U$ together with a regular function on~it. On the one hand, one tries to mimic the case of a germ of holomorphic function in its Miln
Externí odkaz:
http://arxiv.org/abs/2311.01874
Autor:
Sabbah, Claude
Publikováno v:
Documenta Mathematica 28 (2023), no. 6, pp. 1473-1492
We illustrate the Arinkin-Deligne-Katz algorithm for rigid irreducible meromorphic bundles with connection on the projective line by giving motivicity consequences similar to those given by Katz for rigid local systems.
Comment: 19 pages. V2: 20
Comment: 19 pages. V2: 20
Externí odkaz:
http://arxiv.org/abs/2212.07746
Autor:
Sabbah, Claude
This article surveys various duality statements attached to a pair consisting of a smooth complex quasi-projective variety and a regular function on it. It is dedicated to the memory of Bumsig Kim.
Comment: 23 pages. V2: Proof of Proposition 5.2
Comment: 23 pages. V2: Proof of Proposition 5.2
Externí odkaz:
http://arxiv.org/abs/2212.07745
Autor:
Sabbah, Claude, Schnell, Christian
We analyze the behavior of polarized complex variations of Hodge structure on the punctured unit disk. For integral variations of Hodge structure, this analysis was first carried out by Wilfried Schmid. We get rid of the assumption that the eigenvalu
Externí odkaz:
http://arxiv.org/abs/2206.08166
Publikováno v:
Compositio Math. 159 (2023) no. 7, 1413-1465
We develop the theory of relative regular holonomic D-modules with a smooth complex manifold S of arbitrary dimension as parameter space, together with their main functorial properties. In particular, we establish in this general setting the relative
Externí odkaz:
http://arxiv.org/abs/2203.05444
Autor:
Sabbah, Claude, Yu, Jeng-Daw
Publikováno v:
Tunisian J. Math. 5 (2023) 215-271
We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure in the sens
Externí odkaz:
http://arxiv.org/abs/2112.13405
Autor:
Sabbah, Claude
Publikováno v:
Portugaliae Mathematica 79 (2022), no. 1, p. 29-43
We give a short proof of a theorem of G. Cotti, B. Dubrovin and D. Guzzetti (arXiv:1706.04808 and arXiv:2101.03397) asserting the vanishing of some entries of the Stokes matrices at coalescing points of an isomonodromic deformation.
Comment: 11
Comment: 11
Externí odkaz:
http://arxiv.org/abs/2103.16878
We extend to the category of relative regular holonomic modules on a manifold $X$, parametrized by a curve $S$, the Hermitian duality functor (or conjugation functor) of Kashiwara. We prove that this functor is an equivalence with the similar categor
Externí odkaz:
http://arxiv.org/abs/2012.15171